They said he was criticised because the report's authors needed to place blame on a senior officer.

Meanwhile, the BBC's legal affairs analyst has said any decision on prosecutions following the report would be complicated.

Thirteen marchers were shot dead on 30 January 1972 in Londonderry when British paratroopers opened fire on crowds at a civil rights demonstration.

Fourteen others were wounded, one later died.

Col Wilford, who commanded First Battalion Parachute Regiment (1 Para) on Bloody Sunday, has always maintained that his soldiers were fired on first and were merely doing their duty.

However, the Saville report criticised his actions, saying he should not have launched the incursion into the Bogside area of the city.

It said he was wrong to do so because he disobeyed the orders given by his superior, Brigadier Pat McClellan, and also because his soldiers, whose job it was to arrest rioters, would have no or virtually no means of distinguishing them from those who had been involved in the march.

Analysis

By Norman SmithChief political correspondent, BBC Radio 4

A genuine apology can be a powerful political weapon - but one that politicians have tended to shy away from for fear of being seen as weak or in the wrong.

However David Cameron's apology in the commons for Bloody Sunday maybe crucial in helping to convince many of the families not to pursue legal action against the paratroopers.

Indeed, in extraordinary scenes Mr Cameron was actually applauded and cheered by the families and their supporters as they watched him on a huge screen outside Derry's Guildhall deliver an uncompromising condemnation of the "unjustified and unjustifiable" action of British soldiers.

One lawyer suggested that had Mr Cameron in any way sought to justify the conduct of British paratroopers then the likelihood was that the soldiers would have been pursued by the families through the civil courts.

And so - Mr Cameron's intervention, coupled with the strength of the report, would appear to have convinced many of the families that they have secured what they wanted, namely the vindication of their loved ones - and that there is no need for soldiers to appear in the dock.

It said he was also wrong to send soldiers into an unfamiliar area where there was risk of attack from republican paramilitaries, in circumstances where the soldiers' response would risk civilians being killed or injured by army gunfire.

In a statement to the BBC Northern Ireland Spotlight programme, the six soldiers rejected the criticism of Col Wilford.

They said they believed the report had to blame somebody of rank and Col Wilford would do.

The inquiry also directed some criticism at Major General Robert Ford, at the time the second most senior officer in Northern Ireland.

He is singled out by Saville for deploying paratroops to Derry in the first place.

The report states: "1 Para was a force with a reputation for using excessive physical violence, which thus ran the risk of exacerbating the tensions between the army and nationalists in Londonderry."

However it adds that Major General Ford did not have reason to believe that there was significant risk soldiers would open fire unjustifiably.

The inquiry also refers to a memorandum written by Major General Ford in which he suggested shooting selected ringleaders of rioters after warnings.

Saville expresses surprise that a senior officer would consider such a move but adds that he believes the killings were not as a result of the plans.

Following the publication of the report, Prime Minister David Cameron said what happened on Bloody Sunday was wrong and that he was "deeply sorry".

The BBC's legal affairs correspondent Clive Coleman said that, despite the findings, it would not be straightforward to bring prosecutions.

He said there needed to be sufficient evidence to provide a reasonable prospect of conviction - not an easy test after 38 years.

"If any defendant believes that the passage of time makes a fair trial impossible, they could argue the prosecution was an abuse of process," our correspondent said.

"Any prosecutions would also need to be judged to be in the public interest."

Following the report, the decision to prosecute any individual soldier rests with Northern Ireland's Public Prosecution Service (PPS).

In a statement, the PPS said its director and Chief Constable Matt Baggott would consider the report to determine the nature and extent of any police investigations.

Speaking on Tuesday in the House of Commons, Mr Cameron said:

No warning had been given to any civilians before the soldiers opened fire

None of the soldiers fired in response to attacks by petrol bombers or stone throwers

Some of those killed or injured were clearly fleeing or going to help those injured or dying

None of the casualties was posing a threat or doing anything that would justify their shooting

Many of the soldiers lied about their actions

The events of Bloody Sunday were not premeditated

Northern Ireland's Deputy First Minister Martin McGuinness, Sinn Fein, was present at the time of the violence and "probably armed with a sub-machine gun" but did not engage in "any activity that provided any of the soldiers with any justification for opening fire"

Meanwhile the Shadow Northern Ireland Secretary, Shaun Woodward, has suggested the government set up a permanent organisation that would work out of the public eye to try to settle grievances from the Troubles and provide reconciliation.

'Legacy issues'

He said the time was right for "a comprehensive process" because the current way of dealing with the past in Northern Ireland was not effective.

When he was Secretary of State in the last government Mr Woodward received a government-commissioned report on dealing with the past.

It made recommendations about setting up a legacy commission which would deal with all outstanding issues from the Troubles over a five year period.

However, the proposal became bogged down in controversy over a proposal that the families of all those killed during the Troubles should receive a one-off "recognition payment" of £12,000.

That would have meant the families of police officers and soldiers killed by paramilitaries being treated in the same way as the relatives of republican and loyalist paramilitaries.

Mr Woodward rejected that proposal and there has since been little progress on dealing with so-called "legacy issues".